维诺梯度随机晶格结构多尺度设计及实验验证  

Multiscale design and experimental verification of Voronoi graded stochastic lattice structures for the natural frequency maximization problem

作　　者：陈炼雄 潘宇 楚锡华 刘辉 王新忠 Lianxiong Chen;Yu Pan;Xihua Chu;Hui Liu;Xinzhong Wang(School of Civil Engineering,Wuhan University,Wuhan 430072,China;State Key Laboratoryof Structural AnalysisforIndustrialEquipment,Dalian University ofTechnology,Dalianl600,China;Department of Electronic Communication and Technology Shenzhen Institute of Infomation Technology Shenzhen 518000,China)

机构地区：[1]不详

出　　处：《Acta Mechanica Sinica》2023年第8期121-136,共16页力学学报（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant Nos.12072242 and 12172263);the Natural Science Foundation of Hubei Province(Grant No.2020CFB816).

摘　　要：增材制造技术凭借其生产几何复杂结构(如晶格结构)的能力而广受欢迎.在航天航空和汽车领域轻量化设计中,晶格结构具有极大的优势.众所周知,振动问题是航天航空结构设计广泛关注的问题之一,为了避免结构动力破坏,有必要开展结构振动频率研究,尤其是结构自振频率研究.本文针对一阶频率最大化问题,提出了一种维诺梯度随机晶格结构多尺度优化设计方法.首先,在微观尺度上进行了维诺随机晶格微观结构生成和分析.然后,采用无惩罚密度法进行宏观结构优化.最后,基于得到的相对密度分布和映射关系,重构了全尺度维诺梯度随机晶格结构.数值算例验证了该方法在维诺梯度随机晶格结构设计中的正确性和有效性,振动试验也验证了所提出的多尺度方法的有效性和优化的梯度晶格结构在结构动力响应方面的优势.Additive manufacturing(AM)has gained popularity for its capacity to produce geometrically complicated structures,such as lattice structures.Lattice structures have great advantages in the lightweight design of the aerospace and automotive field,in which frequent vibration is one of the most concerning problems during the structure design process.Consequently,it is necessary to research structural vibration frequency to avoid dynamic failure,especially the natural vibration frequency of the structure.In this work,a multiscale topology optimization method is proposed to design the Voronoi graded stochastic lattice structures for the first-order frequency maximization problem.Firstly,the generation and analysis of the Voronoi stochastic lattice microstructure are carried out on the microscale.Then,the macroscale structural optimization is conducted with a penalty-free density method.Finally,the full-scale Voronoi graded stochastic lattice structure is reconstructed based on the obtained relative density distribution and mapping relationship.Numerical examples are performed to demonstrate the correctness and validity of the proposed method for designing the Voronoi graded stochastic lattice structure.Several dynamic experiments also verify the effectiveness of the developed multiscale method and the advantage of the optimized graded lattice structure in structural dynamic response.

关 键 词：晶格结构 最大化问题 多尺度方法 结构自振频率 结构动力响应 密度法 微观尺度 结构设计 

分 类 号：O3[理学—力学]